Entropies for coupled harmonic oscillators and temperature

We study two entropies of a composed system of two coupled harmonic oscillators, which using a heat bath at a temperature T, are brought to a canonical thermal equilibrium. Using the purity function, we explicitly determine the Rényi and von Neumann entropies in terms of different physical parameters. We will numerically analyze these two entropies under suitable conditions, and show their relevance.